Astronomy and Astrophysics – Astrophysics
Scientific paper
Sep 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005ap%26ss.299...67p&link_type=abstract
Astrophysics and Space Science, Volume 299, Issue 1, pp.67-81
Astronomy and Astrophysics
Astrophysics
3
Restricted Three-Body Problem, Angular Velocity, PoincarÉ, Surface Of Section, Periodic Orbit, Non-Linear Stability
Scientific paper
We study the equilibrium points and the zero-velocity curves of Chermnykh’s problem when the angular velocity ω varies continuously and the value of the mass parameter is fixed. The planar symmetric simple-periodic orbits are determined numerically and they are presented for three values of the parameter ω. The stability of the periodic orbits of all the families is computed. Particularly, we explore the network of the families when the angular velocity has the critical value ω = 2√2 at which the triangular equilibria disappear by coalescing with the collinear equilibrium point L1. The analytic determination of the initial conditions of the family which emanate from the Lagrangian libration point L1 in this case, is given. Non-periodic orbits, as points on a surface of section, providing an outlook of the stability regions, chaotic and escape motions as well as multiple-periodic orbits, are also computed. Non-linear stability zones of the triangular Lagrangian points are computed numerically for the Earth Moon and Sun Jupiter mass distribution when the angular velocity varies.
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